Mathematics · 2020
JEE Main · 2 September 2020, Shift 1 · Q59
If a function f(x) defined by f(x)= {ae^x+ be^-x, -1 ≤ x<1; cx^2, 1 ≤ x ≤ 3; a x^2+2 c x, 3<x ≤ 4} be continuous for some a, b, c ∈ R and…
If a function $\displaystyle f(x)$ defined by
$$f(x)= \begin{cases}\mathrm{ae}^x+\mathrm{be}^{-x}, & -1 \leq x<1 \\ \mathrm{cx}^2, & 1 \leq x \leq 3 \\ \mathrm{a} x^2+2 \mathrm{c} x, & 3<x \leq 4\end{cases}
$$
be continuous for some $\displaystyle \mathrm{a}, \mathrm{b}, \mathrm{c} \in \mathbf{R}$ and $\displaystyle f^{\prime}(0)+f^{\prime}(2)=\mathrm{e}$, then the value of $\displaystyle \mathbf{a}$ is :
Official answer
(1)
$\displaystyle \frac{e}{e^2-3 e+13}$
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JEE Main 2020 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.